Week 3
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Due DateJune 1, 2:59 AM EDT
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Due Jun 1, 2:59 AM EDT
What properties does a subset of a vector space L have to have in order to be a subspace:
Find the length of x=(1−73). x is a vector in Euclidean space.
Find the angle between x and y, if x=(1−30)T,y=(01−7)T x, y are vectors in Euclidean space.
Find the dot product ⟨x,y⟩ if x=⎝⎜⎛9−24⎠⎟⎞ and y=⎝⎜⎛2−52⎠⎟⎞ x, y ∈E.
Given a new basis E′={e1′=i+k,e2′=−i−j,e3′=3k−i}, find x=5i−7j+8k in E'. i,j,k is the standart basis.
Suppose ⎩⎪⎨⎪⎧a1=⎝⎜⎛101⎠⎟⎞,a2=⎝⎜⎛0−11⎠⎟⎞⎭⎪⎬⎪⎫ is a basis in L⊂E and x=⎝⎜⎛112⎠⎟⎞,x∈E. Find prLx.
Find the approximation to the solution of Ax=b, where A=⎝⎜⎛310−5−71⎠⎟⎞ and b=⎝⎜⎛025⎠⎟⎞. Use least squares method.